Cyberstuck

I think it would be more correct to phrase it as the rate of change of speed, not the change of rate of speed, as observed in your second line. Nobody would say "change of rate of distance" unless they were a lunatic and I don't see a reason to make a special exception for the word speed.

To dig deeper, the language we use has pretty tight ties to maths in this case, we can consider the word change as meaning delta(assuming we are in a discrete context), and rate as meaning "the ratio of the following quantity with time". (Side note, this is very arbitrary - you need to define the context of the time measurement you're talking about)

• "Rate of speed" would be the ratio of speed:time, which is just the... Average acceleration over the entire measured period, I guess? and so is unsuitable in the OP (unless they mean to say that the driver accelerated a high amount in this period, as opposed to just driving at a high speed)
• Change of rate of speed would be delta speed:time, which would be how the above quantity changed between two measurements, I guess. Average acceleration before vs average acceleration after some arbitrary point?
• Rate of change of speed is then the ratio of delta speed:time, which would be a measure of the average change of speed over some period.

The above 3 are dimensionally identical (all being metres per second squared) but I'd argue their phrasing implies the 3 distinct contexts described above. And none of them are appropriate for describing the speed of a vehicle.